Geospatial exposure modeling methods and applications in human health

Author
Affiliations

Kyle P Messier, PhD

Stadtman Tenure Track Investigator

National Institute of Environmental Health Sciences

Division of Translational Toxicology

ENVR 500 Guest Lecture: February 22, 2024

About Me

  • BS Environmental Science: UNC-Asheville
  • MS, PhD, Environmental Science and Engineering, UNC ESE, Advisor: Marc Serre
  • Postdoc, Environmental Defense Fund, High-Resolution Air Pollution Mapping with Mobile Monitoring
  • Research Faculty, Oregon State University, Department of Environmental and Molecular Toxicology
  • Tenure Track Investigator, NIH/NIEHS/DTT

About Us: {SET}group

  • Spatiotemporal Exposure Mapping
  • Chemical and Stressor Mixtures Prediction
  • Mechanistically Informed Risk Assessment

About Us: {SET}group

  • Eva Marques

  • Daniel Zilber

  • Ranadeep Daw

  • Mariana Alifa

  • Insang Song

  • Kyle Messier

  • Mitchell Manware (Not Pictured)

The Importance of Place

The Importance of Place

  • Hurricane Matthew, 2016
  • Hurricane Florence, 2018
  • Swine Waste Concerns
  • Fecal Bateria
  • Nitrate and Phosphorous Pollution
  • Infectious Diseases

The Importance of Place

https://riskfactor.com/

https://riskfactor.com/

https://riskfactor.com/

https://riskfactor.com/

https://riskfactor.com/

History of Spatial [Geo] Statistics Mining

  • Matheron and Krige developed geostatistical methods to predict ore content from core samples

  • Matheron coined the term “Kriging” after Krige

  • “Nugget” is a term used to random noise because predicting where gold nuggets were was so difficult

History of Spatial [Geo] Statistics: Forestry

  • Matérn developed correlation models for spatial variation for applications in Forestry

  • To this day, we use the “Matérn” covariance function

History of Spatial [Geo] Statistics: Petroleum Engineering

  • Used to evaluate the oil and gas field reservoirs
  • Uses geology and seismic data

History of Spatial [Geo] Statistics: Public Health

  • Cressie, 1990: Statistics for Spatial Data

  • Waller and Gotway, 2004: Applied Statistics for Public Health Data

  • Wide scale adoption for statisticians and engineers in ecological and human exposure and risk applications

Source and Receptor Geometries

Questions:

  • In figure C, what is an example of geospatial health data geometry at a point? Check all that apply.

  • In figure I, what is an example of geospatial health data geometry at an area? Check all that apply.

Geospatial Health Analysis Overview

graph TD;

    style A fill:#91bcfd , stroke:#333, stroke-width:2px, rounded:true;
    style B fill:#91bcfd , stroke:#333, stroke-width:2px, rounded:true;
    style C fill:#91bcfd , stroke:#333, stroke-width:2px, rounded:true;

    A[Research Question: Exposure and Health Outcome Relationship?] --> B[Preparation of Geospatial Exposure Data];
    A --> C[Preparation of Health Outcome Data];

Geospatial Health Analysis Overview

graph TD;

    style A fill:#91bcfd , stroke:#333, stroke-width:2px, rounded:true;
    style B fill:#91bcfd , stroke:#333, stroke-width:2px, rounded:true;
    style C fill:#91bcfd , stroke:#333, stroke-width:2px, rounded:true;

    A[Research Question: Exposure and Health Outcome Relationship?] --> B[Preparation of Geospatial Exposure Data];
    A --> C[Preparation of Health Outcome Data];
    
    B1[Selection of Exposure Metrics];
    B2[Geospatial Exposure Modeling Strategy];
    B3[Geospatial data collection and integration];
    B4[Geospatial model fitting and calibration];
    

    B --> B1;
    B1 --> B2;
    B2 --> B3;
    B3 --> B4;

Questions:

  • what is an example of a point-level exposure data set? Check all that apply.
  • Which of the following are examples of an area-level exposure data set? Check all that apply.

Geospatial Health Analysis Overview

graph TD;

    style A fill:#91bcfd , stroke:#333, stroke-width:2px, rounded:true;
    style B fill:#91bcfd , stroke:#333, stroke-width:2px, rounded:true;
    style C fill:#91bcfd , stroke:#333, stroke-width:2px, rounded:true;

    A[Research Question: Exposure and Health Outcome Relationship?] --> B[Preparation of Geospatial Exposure Data];
    A --> C[Preparation of Health Outcome Data];
    
    B1[Selection of Exposure Metrics];
    B2[Geospatial Exposure Modeling Strategy];
    B3[Geospatial data collection and integration];
    B4[Geospatial model fitting and calibration];
    
    C1[Selection of health outcome metrics];
    C2[Health outcome data collection and integration: Individual or Population Level];
    C3[Geocoding of Health Outcome Data];

    B --> B1;
    B1 --> B2;
    B2 --> B3;
    B3 --> B4;
    
    C --> C1;
    C1 --> C2;
    C2 --> C3;

Geospatial Health Analysis Overview

graph TD;

    style A fill:#91bcfd , stroke:#333, stroke-width:2px, rounded:true;
    style B fill:#91bcfd , stroke:#333, stroke-width:2px, rounded:true;
    style C fill:#91bcfd , stroke:#333, stroke-width:2px, rounded:true;
    style D fill:#91bcfd , stroke:#333, stroke-width:2px, rounded:true;

    A[Research Question: Exposure and Health Outcome Relationship?] --> B[Preparation of Geospatial Exposure Data];
    A --> C[Preparation of Health Outcome Data];
    
    B1[Selection of Exposure Metrics];
    B2[Geospatial Exposure Modeling Strategy];
    B3[Geospatial data collection and integration];
    B4[Geospatial model fitting and calibration];
    
    C1[Selection of health outcome metrics];
    C2[Health outcome data collection and integration: Individual or Population Level];
    C3[Geocoding of Health Outcome Data];
    
    D[Exposure and Health Outcome Data Integration and Analysis];
    D1[Linkage of Exposure Model with Health Data];
    D2[Prediction of Exposure Model at Health Data Locations];
    D3[Exposure and Health Outcome Model Analysis];
    
    B --> B1;
    B1 --> B2;
    B2 --> B3;
    B3 --> B4;
    
    C --> C1;
    C1 --> C2;
    C2 --> C3;
    
    B4 --> D;
    C3 --> D;
    
    D --> D1;
    D1 --> D2;
    D2 --> D3;

The Landscape of Geospatial Exposure Models

The next section will focus on details of geospatial exposure models

Many types of models are used for geospatial exposure assessment.

  • Proximity

  • Index

  • Land Use Regression

  • Geographically Weighted Regression

  • Kriging and Gaussian Processes

  • Machine Learning

  • Mechanistic Models

  • Satellite Imagery

  • Hybrid / Ensemble Models

Notation: Spatial Random Field

  • \(\mathbf{y}\): A single random variable is denoted by a bold lowercase letter
  • \(\mathbf{Y}\): Spatial Random Field (SRF): A collection of random variables across a spatial domain.
  • SRF provides full, probabilistic characterization of exposure across space
  • SRF is referenced to a real-valued domain with spatial and temporal indices, \(\{\mathbf{Y}(s); s \in \mathbb{R}^2\}\).

A Review of Linear Regression

Response

\[ Y_i \in \{1, ..., n\} \] \(p\) covariates:

\[ X = X_{i1}, ..., X_{ip} \]

The model is :

\[ Y_i = \beta_0 + X_{i1}\beta_1 + , ..., X_{ip}\beta_p \]

  • The mean is a linear combination of the covariates

\[ E(Y_i) = \mu_i = \beta_0 + X_{i1}\beta_1 + ... + X_{ip}\beta_p \]

  • Error/Residuals are assumed to be independent and identically distributed (iid)

\[ \varepsilon_i = Y_i - \mu_i \]

Linear Regression for spatial idea

  • As a method, not a terrible idea

  • Unbiased

  • Overconfident error estiamte (p-values, SE)

  • Model Selection (Type 1 and 2 error)

Land Use Regression

Linear regression for spatial data

\[ \bY(s) = X(s)\beta + \varepsilon \]

\[ X(s) = X_{i1}(s_1), ..., X_{ip}(s_p) \]

Spatial Covariance Model

  • As a random-effect model, we add a spatially explicity error term

\[ \bY(s) = \mu(s) + \varepsilon + \eta(s) \]

  • \(\mu(s)\) can take many forms such as linear, nonlinear, or even machine learning models such as random forest.

  • More details on a spatial covariance model later

Proximity

  • Proximity based metrics are the most basic form of an exposure assessment because they rely only on the distance between a pollution source and the observed outcome location.

  • A proximity model is simply a deterministic covariate based on distance:

\[ Y(s) = X(s) \]

Given a matrix of distances between monitoring locations and pollution sources, \(d_{ij}\), minimum and average distance are:

\[ X_i^{min} = min(d_{i,\cdot}) \\ \overline{X}_i = \frac{1}{n_j}\sum_{j=1}^{n_j}d_{ij}\\ \]

Questions:

  • What are examples of proximity metrics? Check all that apply.
  • What are the advantages of a proximity metric? Check all that apply.

Index Models

  • Index variables are deterministic quantities that summarize (e.g. prinicipal components) multiple complex variables of interest into a simple and interpretable metric.

  • Covariates are made up of geographic variables across different domains

  • Social Vulnerability Index, Climate Vulnerability Index, etc.

Land Use Regression

\[ \bY(s) = X(s)\beta + \varepsilon \] - where \(\bY(p)\) are the \(n \times 1\) observations for the variable of interest (e.g. PM\(_{2.5}\), \(NO_3^{-}\), etc.). \(X(s)\) is a \(n \times k\) design matrix of \(k\) spatial geographic covariates

Key Steps

  1. Calculate geographic covariates
  2. Fit the model - may include model selection or dimension reduction
  3. Predict at unmonitored locations

Geographically Weighted Regression

  • \[ \bY(s) = X(s)\beta(s) + \varepsilon \]
  • What is the key difference between LUR and GWR? Select one. Recall, LUR = \(\bY(s) = X(s)\beta + \varepsilon\)
  • Hint: It’s in the \(\beta\)

Gaussian Process and Kriging

  • Gaussian process and Kriging are one in the same
  • Utilize information on spatial correlation to help interpolate
  • Account for spatial error
  • Highly flexible

Gaussian Process and Kriging

\[ \bY(s) = \mu(s) + \eta(s) \]

  • \(\mu(s)\) can take many forms such as linear, nonlinear, or even machine learning models such as random forest

  • \(\eta \sim N_n(0,\Sigma_{\theta}+\tau^2I)\)

  • \(\Sigma_{\theta}\) is a covariance matrix with parameters, \(\theta\), that accounts for correlation between spatial and temporal locations

Question:

  • What physical quantity is \(\Sigma_{\theta}\) solely dependent on?

Machine Learning

Machine learning (ML) is the general culture, philosophy, or school of thought for predictive modeling that focuses on the learning algorithm and out-of-sample prediction generalization

  • Many common machine learning algorithms can be used for geospatial modeling
  • Flexible
  • Don’t make strict assumptions on the distriubtions of the data
  • Coordinates and other spatial information is input as covariates
  • Common Methods in Exposure Modeling
  • Generalized Additive Models (GAM)
  • Random Forest
  • xgboost
  • Neural Networks: CNN, LSTM, GAN, etc.

Machine Learning: Trees

Mechanistic

  • I would be remiss if I didn’t mention another entirely different class of exposure models

  • Mechanistic models are not statistical models

  • Mechanistic models are based on physics and chemistry

Hybrid

A consensus of multiple models is almost always better than any single model.

Requia, Weeberb J., et al. “An ensemble learning approach for estimating high spatiotemporal resolution of ground-level ozone in the contiguous United States.” Environmental science & technology 54.18 (2020): 11037-11047.

Yu, Wenhua, et al. “Deep ensemble machine learning framework for the estimation of PM 2.5 concentrations.” Environmental Health Perspectives 130.3 (2022): 037004.

Integrating Geospatial Exposure Models into Health Data

graph TD;

    style A fill:#91bcfd , stroke:#333, stroke-width:2px, rounded:true;
    style B fill:#91bcfd , stroke:#333, stroke-width:2px, rounded:true;
    style C fill:#91bcfd , stroke:#333, stroke-width:2px, rounded:true;
    style D fill:#91bcfd , stroke:#333, stroke-width:2px, rounded:true;

    A[Research Question: Exposure and Health Outcome Relationship?] --> B[Preparation of Geospatial Exposure Data];
    A --> C[Preparation of Health Outcome Data];
    
    B1[Selection of Exposure Metrics];
    B2[Geospatial Exposure Modeling Strategy];
    B3[Geospatial data collection and integration];
    B4[Geospatial model fitting and calibration];
    
    C1[Selection of health outcome metrics];
    C2[Health outcome data collection and integration: Individual or Population Level];
    C3[Geocoding of Health Outcome Data];
    
    D[Exposure and Health Outcome Data Integration and Analysis];
    D1[Linkage of Exposure Model with Health Data];
    D2[Prediction of Exposure Model at Health Data Locations];
    D3[Exposure and Health Outcome Model Analysis];
    
    B --> B1;
    B1 --> B2;
    B2 --> B3;
    B3 --> B4;
    
    C --> C1;
    C1 --> C2;
    C2 --> C3;
    
    B4 --> D;
    C3 --> D;
    
    D --> D1;
    D1 --> D2;
    D2 --> D3;

Classical Framework for Geospatial Risk Assessment

graph TB;

    style A fill:#91bcfd , stroke:#333, stroke-width:2px, rounded:true;

    A(Hazard Identification);
    B(External Exposure Assessment) --> |Behaviorial, Physiological, Toxicokinetic Modeling| C(Internal Exposure);
    C --> |Epidemiological Methods| E(Health Effect Assessment);
    E --> |Health Impact Model| F(Health Burden);
    B --> |Epidemiological Methods| E;

Questions

  • The left size of the figure shows an option to calculate internal exposure from a geospatially modeled external exposure. What are some key assumptions in this approach?

Classical Framework for Geospatial Risk Assessment